Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x+4y &= -4 \\ -8x+8y &= 1\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $8y = 8x+1$ Divide both sides by $8$ to isolate $y$ $y = {x + \dfrac{1}{8}}$ Substitute this expression for $y$ in the first equation. $-5x+4({x + \dfrac{1}{8}}) = -4$ $-5x + 4x + \dfrac{1}{2} = -4$ Simplify by combining terms, then solve for $x$ $-1x + \dfrac{1}{2} = -4$ $-1x = -\dfrac{9}{2}$ $x = \dfrac{9}{2}$ Substitute $\dfrac{9}{2}$ for $x$ back into the top equation. $-5( \dfrac{9}{2})+4y = -4$ $-\dfrac{45}{2}+4y = -4$ $4y = \dfrac{37}{2}$ $y = \dfrac{37}{8}$ The solution is $\enspace x = \dfrac{9}{2}, \enspace y = \dfrac{37}{8}$.